Assume you have functions f and g such that f(n) is O(g(n)). For each of the following statements, decide whether you think it is true of false and give a proof or counter-example.

My thoughts are False, True, True. But can someone give proofs?

Assume you have functions f and g such that f(n) is O(g(n)). For each of the following statements, decide whether you think it is true or false and give a proof or counterexample. (a) log2f(n) is O(log2g(n)). (b) 2f(n) is O(2g(n)). (c) f(n)2 is O(g(n)2)